This invention relates to methods of performing gradient computation and, more particularly, to gradient-based methods of performing circuit optimization.
Rapid and automatic optimization (or tuning) of circuits is crucial to high-performance circuit design. Circuit tuning is a nonlinear optimization problem which is best solved by gradient-based methods. The adjoint method, as disclosed in the article by S. W. Director et al., "The Generalized Adjoint Network and Network Sensitivities," IEEE Transactions on Circuit Theory, pp. 318-323, vol. CT-16, no. 3 (August 1969), permits the computation of the gradients of one measurement of the circuit with respect to any number of design parameters by means of a single adjoint analysis. However, the adjoint analysis must be repeated for each measurement of interest. Likewise, the direct method of gradient computation, as disclosed in the article by D. A. Hocevar et al., "Transient Sensitivity Computation for MOSFET Circuits," IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, pp. 609-620, vol. CAD-4 (October 1985), can compute the gradient of all measurements with respect to one design parameter and, therefore, must be repeated for each design parameter. As a result, the gradient computation procedure is often the bottleneck in circuit optimization programs.